In this lesson we began talking about probability. We found that an experiment is a situatin with several possible results and that an outcome is a possible result of an experiment. Also we learned that the sample space is the set of the total number of possible outcomes of an experiment. We must come to understand and become comfortable with what these terms mean for we will be using the vocabulary of our study in math class and it would be best for us not to be too confused. -Allison R.
Probability was the theme of this lesson, like Allison said. Probability is the study of chance using math. We use probability daily in games of chance, especially when we play lthe ottery (when we are old enough of course). There are several vocabulary terms we learn along with probability that you can see in the slide show above that will help us further understand what is being discussed. Also there are two theorems in the slide show we should learn and use in the quiz. -Shelby N.
This lesson deals with addition counting principles and the union or intersection of sets.
Some sets have nothing in common and when this is the case they are called disjoint or mutually exclusive. When they do share things or overlap, the sets intersect. There are a few principles dealing with the union and instersection of sets. Finding the probablity that two events might happen at the same time can be figured out by using the principles. - Mary G.
Correct answer to the bonus: The states that have the continental divide going through them are Montana, Wyoming, Colorado, New Mexico, and Alaska. - Robert M. (The continental divide forms the boundary between Montana and Idaho, but it is technically in Montana, not Idaho.)
In this lesson we learned about factorials and other mathematical endeavors but i am going to talk about selections without replacement. We found that in certain situations we are not able to replace given information back into a situation to pull again because it's taken. For instance in a race how many different possible standing orders are you able to get? Since when one person gets first that spot is taken you can't use it again meaning you can't replace it and the probability of getting that spot is zero. So you have to use the factorial "!" so if you have a seven man race and want to find the size of the sample space you do 7! -allison r.
the multiplication counting principle states that if you have 2 finite sets, the number of ways to choose something from one set then another is to multiply the sample spaces of the 2 events.
example you are choosing between a cheese burger or hamburger you must chose one and then you are choosing between chips, fries or mac and cheese you must chose one so 2x3=6 you have 6 different options for your meal
the selections with replacement theorem states that for any set s with n elements there are n^k possible arrangements of k elements fro m s with replacement ( the sample space stays the same)
example a true and false test you have 2 options for your answer and if there are 5 questions then 2x2x2x2x2=2^5 or 32 and then put that under one
alyssa w.
A permutation is a particular arrangement of elements of a set where order matters. A theorem is included and it says that if there are n elements of a set, there are n! permutations of those elements. This really is helpful when you are just using part of the set but the order in which they are selected matters. A formula to solve permutations is nPr=n!/(n-r)!.
Jeremy G.
Permutations is the arrangement of objects in different orders, in which the order matters. Equations: ; where n is the total number of objects and r is the number of objects chosen.
0!=1 Applications:
Say you have 8 books you want to arrange of your Book shelf. How many ways can your arrange them?
So there are 40320 ways you can arrange your books on your book shelf. austin a.
In Lesson 7-5, the concept of independent and dependent events were covered. An INDEPENDENT EVENT is a situation in which the result of one event does not affect the results of another event. For instance, when a coin is tossed, the result of that toss has no effect, or is independent of another toss; so coin tosses is an independent event situation. Selections WITH REPLACEMENT are considered to be independent events because later selections do not "remember" what happened with earlier selections. The definition of independent events is as follows: Events A and B are independent events if and only if P(A intersection B) = P(A)*P(B).
When the value of the probability of a certain event depends on the outcome of a different event, the situation is said to be a DEPENDENT EVENT. So, selections without replacement are considered to be dependent. In a situation with dependent events, P(A intersection B) DOES NOTEQUAL P(A)*P(B). Also, it is important to note that events which have a nonzero probability of occurring cannot be both independent and mutually exclusive.
AUSTIN J. R.
Lesson 7-5
Independent Events:
Events A and B are INDEPENDENT IFF the probability of A times the probability of B is equal to the Probability of A intersection of B. When the probabilities value of an event depends on the outcomes of a different event, then that situation is assumed to a DEPENDENT Events. In simpler terms if events A and B are dependent, then the probability of A intersection B is not equal to the probability of A times the probability of B. Events without replacement are said to be dependent. Events with a nonzero probability cannot be both independent and mutually exclusive as stated in the Idea of the presidential race on page 454.
Table of Contents
Chapter 7: Probability and Simulation
7-1: Basic Principles of Probability
In this lesson we began talking about probability. We found that an experiment is a situatin with several possible results and that an outcome is a possible result of an experiment. Also we learned that the sample space is the set of the total number of possible outcomes of an experiment. We must come to understand and become comfortable with what these terms mean for we will be using the vocabulary of our study in math class and it would be best for us not to be too confused. -Allison R.
Probability was the theme of this lesson, like Allison said. Probability is the study of chance using math. We use probability daily in games of chance, especially when we play lthe ottery (when we are old enough of course). There are several vocabulary terms we learn along with probability that you can see in the slide show above that will help us further understand what is being discussed. Also there are two theorems in the slide show we should learn and use in the quiz. -Shelby N.
7-2: Addition Counting Principles
This lesson deals with addition counting principles and the union or intersection of sets.
Some sets have nothing in common and when this is the case they are called disjoint or mutually exclusive. When they do share things or overlap, the sets intersect. There are a few principles dealing with the union and instersection of sets. Finding the probablity that two events might happen at the same time can be figured out by using the principles. - Mary G.
Correct answer to the bonus: The states that have the continental divide going through them are Montana, Wyoming, Colorado, New Mexico, and Alaska. - Robert M. (The continental divide forms the boundary between Montana and Idaho, but it is technically in Montana, not Idaho.)
7-3: Multiplication Counting Principles
In this lesson we learned about factorials and other mathematical endeavors but i am going to talk about selections without replacement. We found that in certain situations we are not able to replace given information back into a situation to pull again because it's taken. For instance in a race how many different possible standing orders are you able to get? Since when one person gets first that spot is taken you can't use it again meaning you can't replace it and the probability of getting that spot is zero. So you have to use the factorial "!" so if you have a seven man race and want to find the size of the sample space you do 7! -allison r.
the multiplication counting principle states that if you have 2 finite sets, the number of ways to choose something from one set then another is to multiply the sample spaces of the 2 events.
example you are choosing between a cheese burger or hamburger you must chose one and then you are choosing between chips, fries or mac and cheese you must chose one so 2x3=6 you have 6 different options for your meal
the selections with replacement theorem states that for any set s with n elements there are n^k possible arrangements of k elements fro m s with replacement ( the sample space stays the same)
example a true and false test you have 2 options for your answer and if there are 5 questions then 2x2x2x2x2=2^5 or 32 and then put that under one
alyssa w.
7-4: Permutations
A permutation is a particular arrangement of elements of a set where order matters. A theorem is included and it says that if there are n elements of a set, there are n! permutations of those elements. This really is helpful when you are just using part of the set but the order in which they are selected matters. A formula to solve permutations is nPr=n!/(n-r)!.
Jeremy G.
Permutations is the arrangement of objects in different orders, in which the order matters.
Equations:
0!=1
Applications:
Say you have 8 books you want to arrange of your Book shelf. How many ways can your arrange them?
So there are 40320 ways you can arrange your books on your book shelf. austin a.
7-5: Independent Events
In Lesson 7-5, the concept of independent and dependent events were covered. An INDEPENDENT EVENT is a situation in which the result of one event does not affect the results of another event. For instance, when a coin is tossed, the result of that toss has no effect, or is independent of another toss; so coin tosses is an independent event situation. Selections WITH REPLACEMENT are considered to be independent events because later selections do not "remember" what happened with earlier selections. The definition of independent events is as follows: Events A and B are independent events if and only if P(A intersection B) = P(A)*P(B).
When the value of the probability of a certain event depends on the outcome of a different event, the situation is said to be a DEPENDENT EVENT. So, selections without replacement are considered to be dependent. In a situation with dependent events, P(A intersection B) DOES NOT EQUAL P(A)*P(B). Also, it is important to note that events which have a nonzero probability of occurring cannot be both independent and mutually exclusive.
AUSTIN J. R.
Lesson 7-5
Independent Events:
Events A and B are INDEPENDENT IFF the probability of A times the probability of B is equal to the Probability of A intersection of B. When the probabilities value of an event depends on the outcomes of a different event, then that situation is assumed to a DEPENDENT Events. In simpler terms if events A and B are dependent, then the probability of A intersection B is not equal to the probability of A times the probability of B. Events without replacement are said to be dependent. Events with a nonzero probability cannot be both independent and mutually exclusive as stated in the Idea of the presidential race on page 454.
Troy L.
7-6: Probability Distributions
7-7: Designing Simulations and 7-8: Simulations with Technology
Stick or Switch
Calendar